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arxiv: 1210.3520 · v1 · pith:YKH3JO7Jnew · submitted 2012-10-12 · 🧮 math.RA

Distributive lattices determined by weighted double skeletons

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keywords skeletonlatticeseconddistributivedoublefiniteintroducedweighted
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Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive lattice and its second skeleton, S(S(D)), is the trivial lattice, then D is characterized by its weighted double skeleton, introduced by the second author in 2006. The assumption on the second skeleton is essential.

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